Math 1313 Section 1.5
Linear Cost, Revenue and Profit Functions: If x is the number of units of a product manufactured or sold at a firm then, The cost function, C(x), is the total cost of manufacturing x units of the product. Fixed costs are the costs that remain regardless of the company’s activity. Examples: building fees (rent or mortgage), executive salaries Variable costs are costs that vary with the production or sales. Examples; wages of production staff, raw materials The revenue function, R(x), is the total revenue realized from the sale of x units of the product. The profit function, P(x), is the total profit realized from the manufacturing and sale of the x units of product. Formulas: Suppose a firm has fixed cost of F dollars, production cost of c dollars per unit and selling price of s dollars per unit then C(x) = R(x) = P(x) = Where x is the number of units of the commodity produced and sold. Example 3: A manufacturer has a monthly fixed cost of $150,000 and a production cost of $18 for each unit produced. The product sells for $24 per unit. a. What is the cost function? b. What is the revenue function? c. What is the profit function? d. Compute the profit (loss) corresponding to production levels of 22,000 and 28,000.